SRV-23

Map representative fraction

RF = d / D = 1 : (D/d). Ground distance D for map distance d.

Reading speed

MapsRF

Governing equation

\mathrm{RF}=d/D

$D \in \left[5, 20000\right]$

where

d: Map distance (mm)
D: Ground distance (m)
RF: Representative fraction (—)
1:N: Scale denominator (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\mathrm{RF}=d/D

$D \in \left[5, 20000\right]$

$D = 5$ $RF = 125$

Along the curve

②

Domain of the variable — blue

D_{\min} = 5,\quad D_{\max} = 20000

$D \in \left[5, 20000\right]$

$D = 5$ $D = 5$

Along the curve

③

Response curve — green

\mathrm{RF}=d/D

$D \in \left[5, 20000\right]$

$D = 5$ $RF = 125$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}RF}{\mathrm{d}D}

$D \in \left[5, 20000\right]$

$D = 130.8$ $RF^{\prime} = 25$

Along the curve

Lecture brief

Historical brief

From chain and theodolite through Bowditch’s compass-rule (1802) to GPS PDOP, surveying is the propagation of small errors across a network. These sheets close traverses, reduce stadia and state map scale. This sheet (SRV-23 — Map representative fraction) is the form associated with RF. Working symbols: $d$ , $D$ $\rightarrow$ $RF$ , $1:N$ . A dimensionless scale. Large-scale maps (1:500) show more detail than small-scale (1:50 000).

Purpose

Purpose: compute

RF

1:N

from

d

D

in Surveying via

\mathrm{RF}=d/D

RF = d / D = 1 : (D/d). Ground distance D for map distance d. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

d = 40.000\,\mathrm{mm}

D = 200.000\,\mathrm{m}

, the governing relation

\mathrm{RF}=d/D

yields

RF = 2.000e-4\,\mathrm{—}

1:N = 5000\,\mathrm{—}

. A map bar, a ground tape, a ratio. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Map distance d40 mmGround distance D200 m

Outputs

Representative fraction RF0.000200 —
Scale denominator 1:N5000 —

Reading speed

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Narration of this film

A map bar, a ground tape, a ratio.

A dimensionless scale. Large-scale maps (1:500) show more detail than small-scale (1:50 000).

Reading speed

Watch on YouTube